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Global Non-Negative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems

Global Non-Negative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems

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Prüfsumme: MD5:8ab71257189f4256affb31c812459d3c

JÜNGEL, Ansgar, René PINNAU, 1999. Global Non-Negative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems

@unpublished{Jungel1999Globa-6208, title={Global Non-Negative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems}, year={1999}, author={Jüngel, Ansgar and Pinnau, René} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/6208"> <dc:contributor>Pinnau, René</dc:contributor> <dc:format>application/pdf</dc:format> <dc:creator>Jüngel, Ansgar</dc:creator> <dc:rights>deposit-license</dc:rights> <dcterms:abstract xml:lang="eng">The existence of non-negative weak solutions globally in time of a nonlinear fourth-order parabolic equation in one space dimension is shown. This equation arises in the study of interface fluctuations in spin systems and in quantum semiconductor modeling. The problem is considered on a bounded interval subject to initial and Dirichlet and Neumann boundary conditions. Further, the initial datum is only assumed to be non-negative and to satisfy a weak integrability condition. The main difficulty of the existence proof is to ensure that the solutions stay non-negative and exist globally in time. The first property is obtained by an exponential transformation of variables. Moreover, entropy-type estimates allow for the proof of the second property. Results concerning the uniqueness and long-time behaviour are given and the multi-dimensional problem is discussed. Finally, numerical experiments underlining the preservation of positivity are presented.</dcterms:abstract> <dc:contributor>Jüngel, Ansgar</dc:contributor> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T16:10:13Z</dcterms:available> <dcterms:title>Global Non-Negative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems</dcterms:title> <dc:creator>Pinnau, René</dc:creator> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103416863-3868037-7"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T16:10:13Z</dc:date> <dcterms:issued>1999</dcterms:issued> <dc:language>eng</dc:language> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/6208"/> </rdf:Description> </rdf:RDF>

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

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